Show that T,+M, = S2n- Mn=S2n-

Q: 7. Determine the coefficients a, b, c and d so that the curve y = ax* + bx³ + cx² + dx + e will pass…

A: Given a function of the curve, y=ax4+bx3+cx2+dx+e To find the coefficient a,b,c, and d such that the…

Q: 2 3/2 between x = 0 and x = 1 is 3 %3D The length of the curve y =

A: We will find out the length of curve.

Q: 4/2 % for 0 sxsl. Find the length of the curve y+1=- 3

A: The equation is y+1=423x3/2.   Differentiate with respect to x.…

Q: Find the length of the curve. 9) The spiral r = 202, 0 s 0 s 2^/3

A:

Q: 3. Determine the coefficients a, b, c, d that will make the curve y = ax³ + bx? + cx +d have…

A: We will find the value of a, b, c, and d as following .

Q: The temperature in degrees centigrade (°C) at each point (x, y) on a curve 2x + y = 3 is given by…

A:

Q: Q4/ Find the abs.max cand abs, min Valuse of the Runctia Kcx, y) = I+xy-3x on the closed regen…

A: We have f(x, y) = 1+xy-3x ∂f∂x = y-3, ∂f∂x = 0, y-3 = 0, y = 3 ∂f∂y = x, ∂f∂y = 0, x=0 So one…

Q: 4.) y = VT, y = 3, x = 0 around the y axis %3D

A: Given, y = x1/2, y = 3, x = 0, we have to find the volume by rotating about the y-axis.

Q: Find the family of oblique trajectories that intersect the family of the paraboles y = Cx at angle e…

A:

Q: Find the length of the curve 4t2 -1 dt, y = %3D 1<x<3 8. 15 104 3 3.

A:

Q: Find the plane thst passes through the equation of. the point P(6,0,-2) ¢ = 1+t, z=2 -t entains the…

A:

Q: Find the length of the curve y =/2 from z = 0 to z = 3. %3D

A: Integration of (1+(f'(x))2)1/2 form 0 to.3

Q: Determine the coefficients a, b, c, and d so that the curve will satisfy the stipulated condition.…

A: Given curve is y=ax3+bx2+cx+d        (1) and critical points are (1, 0) and (-2, 27) We have to find…

Q: c) Find the minimum distance from the point (4,0,6) to the plane x- y +2 = 3

A: The solution is given below. .

Q: 7. Find the length of the curve y = (* Vt3 -1 dt 1<t<4. 12.4

A:

Q: Find the orthogonal trajectories of the family of curves r² + y² = 2my where m is a constant.

A: As given equation of curve is: x2+y2=2my Differentiate it with respect to x:…

Q: (0) X. 人セこトン (242) 27 vay 4th 15 where Cis the path from P(0,0 to evaluate つlxe し use Green's…

A:

Q: Q2: A-The Trapezoidal rule for roodx 5 and Midpoint rule /)dx=4 What value does . Simpsons rule give…

A: 1st we will find relation between trapizoidal , mid point and simpson rule . Then will use this…

Q: 2) Consider the oriented curve C given by C = C1uC2, where C2 is obtained by intersecting the…

A: We will first parametrize the curves C1 &amp; C2 then substitute the x,y,z values into the line…

Q: What is the shortest distance from the point (4,0, 5) to the sphere (x – 1)2 + (y + 2)2 + z² = 36?…

A:

Q: Show that the function (x2+y2 t224이) is a Solution of Loplace's equation d2u dy?

A: It will be solution of given Laplace equation only when, it will satisfy it.

Q: e length of the curve y = V 4 – x2, 0 <x< 2. ing the shape of the curve.

A: Use the arc length formula to find the length of the curve.  y=(4-x2)1/2 , 0&lt;=x&lt;=2

Q: b) If we are at the point (1, 2, 4) on the surface z = xy², and we move a short distance in the…

A: Please check step 2 for solution.!

Q: 3. Find the family of oblique trajectories that intersect the family of the paraboles y =cx at angle…

A: given family of parabolas y2=cx at angle θ=60° claim- find the family of oblique trajectories that…

Q: Find the coordinates of the point(s) on the curve y = Va + 3 that are closest to the point (8, 0).…

A: Given problem:- Find the coordinates of the point(s) on the curve y = √(x + 3) that are closest to…

Q: Find the point P nearest to Q = (−1, 3, −1) on the planex − 4z = 2

A:

Q: 2. At time t sec, the positions of two particles A andB on a horizontal coordinate line are sA = 3t3…

A:

Q: 5) 3 = f(x) impending , 8y? = x2-x", ± sx r3 fomd Coleu lete the sunfoce orea of the y roteting…

A: We are given that 8y2 = x2 - x4 and 1/√3 ≤ x ≤ 1/√2. We need to calculate the surface area of the…

Q: The length of the curve y = (2+ 2x )3/2 between x=0 and x=2 is O 41/3 O 45/2 O 43/2 O 47/3 49/6 ООО…

A:

Q: 13. Find the length of the curve y4 + 8 from y = 1 to y = 4. X = 4y2

A: To find the length of given curve.

Q: Find the length of the curve 3x = (y² + 2)³/2 from y = 2 to y = 3 %3D

A: Use length of curve formula:-  for a given curve x = f(y) from y=y1 to y=y2 length of curve,…

Q: 3. For the curve x – xy² = 8e²4, do the following | a) Verify that the point (2,0) is on this curve.

A: Given, curve x3-xy2=8e2y

Q: 4 Find the length of the curve y=x3 3 %3D x3 +5, 1 Record Audio Record Video Add a File

A: To find out the length of the curve.

Q: Q4/Find the abs.max and abs.min valuse of the huctu f,y) = \+xy-3x on the cosol regen oounded by the…

A:

Q: 3/2 The length of the curve x= 4y2 from y=1 to y= 4 is given by

A:

Q: Determine the coefficient a, b ,c and d so that the cruve will satisfy the stipulated condition.…

A:

Q: Suppose that the Celsius temperature at the point (x, y, z) on the sphere x2 + y2 + z2 = 1 is T =…

A: We have given; The temperature T at any point (x, y, z) in space isT = 400xyz2and the unit spherex2…

Q: 1. Find the are length of the curve x = (y + 2)2 from y-0 to y=1

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: A train is moving at 15 m/s, while steam is shut off and brakes are applied. The speed of the train…

A: Consider the continuous function f(x) defined on an interval a,b. Then the Trapezoidal rule…

Q: An automobile, traveling at a constant rate, starts at home at ime t = 0 and ends up 10 hours later…

A:

Q: SOLVE STEP BY STEP Evaluate the length of the curve x = 5 - Vy+1 , 0<ys 3

A:

Q: 27 hPlans that pas Ses through the Point C60,27 and contains the like メt4-2t)ソ= 34st) Zzス+4t 7.

A: Recall: General equation of a plane :     An equation for the plane through (x0, y0,z0 ) and…

Q: What are the critical points for the plane curve defined by the equations æ(t) = sint + cos(t), y(t)…

A: Critical points.

Q: Determine the location of a point (x, y, z) that satisfies the condition(s). xy &gt; 0, z = −3

A: Here Our Aim is to determine the location of a point (x,y,z) that satisfiesthe condition(s):→…

Q: dx Calculate for n = 6, using trapezoidal rule. %3D -11+ x²

A:

Q: Find the family of oblique trajectories that intersect the family of the paraboles y =cx at angle 0…

A:

Q: find the location of a point xyz that satisfies the condition I) xy<0, z=3 ii) |x|<2

A:

Q: Find the family of oblique trajectories that intersect the family of the paraboles y =cx at angle e…

A: The answer is given below:

Q: FInd c and d so that the curve y = x3+ cx2+d will have a relative extrema at (2,5). Find other…

A: Maxima or minima: Let f(x) is any function. 1) Evaluate f'(x) = 0 for critical point. 2) Evaluate…

Q: EX Find the point the curve y=x3+x²-l where the tamjent on is parallel to the X-oaxis

A:

Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.